How about the RX100 M1 or the G7X M1?
Either can be gotten below $200 used. Both have usable autofocus and usable 30/60fps 1080p
The G7X has a 3 stop ND filter and a touchscreen and it will achieve the same level of background blurriness as an APS-C kit lens while having 100mm FF equivalent focal length.
They are both pocketable and cheap enough to not worry about losing them/theft
Both don't have mic ports though

The follow focus will probably be no different from their current implementation of the zoom control which uses USB PTP instead of wifi. This won't be a relevant feature for the majority of Panasonic users as only the GH4/5 and GX8 support control over PTP.
On another note, besides releasing a new gimbal every few weeks, Zhiyun could easily release an SDK for their bluetooth gimbal controls, this could probably lead to more creative control for end users (like damped movement simulating a fluid head) and perhaps other uses Zhiyun themselves haven't thought of.

I've spent a day converting the existing GX80 Cinelike-D hack html file into an Android APK. There's an added color temperature function.
This app should yield some usability advantages as it allows on the fly changes to the various picture profile settings and contains all settings on a single page. It also saves your last selected settings.
Notes on installation:
-Allow installation of apps from unknown sources
Instructions for use:
1. Connect to your camera's wifi network
2. Start the app
3. Click handshake (ignore any update warnings)
4. Click recmode
5. Change settings before or while filming
Other notes:
1. The app may erase existing settings saved in your various picture profiles
2. Camera IP selection is not yet implemented, apologies to those who do not connect to their cameras directly
3. Tested on a G7
Download link: https://github.com/lippyt/lumixlib/raw/master/lumix.apk

I actually use the property of equality between tele-normal and wide-normal to determine the current focusing distance. I have not tried to deliberately switch between normal and fast modes, though I believe that their focus steps do not share a common denominator so we can definitely get between the cracks that way. Another way is for a user to turn the focusing ring so this generates a non squared-off value, for example he could reach 101,102,103....119,120 depending on luck. Requesting a tele or wide normal after that point will mean that all focus steps will not be similar to their squared-off values.
Certainly, I guess that panasonic gave lesser focus steps at the wide end because its much easier to focus/ the DOF would more than cover up for it. And even the coarse steps in some lenses would be more than sufficient for the focus pulling portion of your camera controller.
As for focus breathing on lenses, the 25mm panasonic lens has a ridiculous 20% scale from near to infinity (non scientific test, a guesstimation when playing with premiere footage).

Meticulous is too little to describe the detail in which you explored this. I feel silly that I did not look at the get-info page for lenses yet.
Yes, by focus steps I am trying to describe the amount of focus positions there are within the 0-1024 range after "squaring-off" the focal distance against closest focusing distance or farthest focusing distance.
For example in the 14-42mm kit lens the focus steps at 14mm (wide-normal) are separated by 11-15 focus bits and at 42mm the focus steps are separated by 6 focus bits. In the 25mm f1.7 the focus steps are separated by 3-4 bits. I realize that focus bits are just virtual figures and probably do have a direct correspondence with true focal distance.
While trying to design a focus ramping time lapse script, I realized that I wanted the true number of focus steps between two points so that I could decide how often to shift focus a step back or forth (or whether to shift focus for more than a step per shot).
I agree that we cannot reach the precise focusing step/bit using the four functions due to the limitations of the wifi requests and that degree of correspondence between a move on a physical control and the rate of transition is important.
(I am going back to try out more scripts, because I have lots more to learn about this wifi system and posting anything else here would be talking out of my ass!)

I want to share a short script I wrote in python that does focus ramping time lapses for Panasonic cameras. I believe this is doable in magic lantern for Canon users but I've yet to see an implementation for Panasonic. Here is a short technical preview:
Here is the python script I used to make this focus rack timelapse:
https://github.com/lippyt/lumixlib/blob/master/focuslapse.py
I'm sure that there are much more creative uses especially for shots with the majority of objects in the near-medium range.

Hi BTM_Pix, love your work with the focus controller!
Would you be doing lens profiling/setup for lenses for this focus racking system? I've done some minor research into how many possible focus steps there are per lens and I found that it varies between lenses and even among different focal lengths on the same zoom lens.
I would believe this will affect the duration of a focus pull depending on how the focus racking code is done.
If you've already considered this, perhaps we could request fellow forumers to share their lens focus step data so that there is a more complete picture as to how focus step varies.
Here is the python file that I wrote for finding lens data: https://github.com/lippyt/lumixlib/blob/master/lensdata.py

Thanks for stating these points. They definitely helps me in organizing my thoughts regarding this issue.
Point taken, I understand the importance of industry links/network of the university. As I am living in South East Asia, the likely destination for me would be Australia.
Sadly, the next biggest potential film market (China) doesn't have a film school that readily admits foreigners, otherwise, I had that in mind as a way of entering the Chinese film industry.

I am quite curious of the opinion of this forum on taking a degree in film.
I understand that many would say its a waste of time and with the wealth of information available online, there is little reason to study film in an institute of higher education. Although individual talent does matter most, I wonder if there are any film school graduates here who can at least provide a positive argument on why going to film school is good or whether you found it a waste of time. Does it help in your employability or ability to see things in the big picture etc?
I'm asking this as I am planning to do a postgrad degree in Film/Media Production and I come from a different field of study.
(hoping this thread sits well, I realize this is a forum mainly for gear!)

No mention of Image Stabilization for both their lenses and body or flat profile on their website and Dpreview's hands-on, could even be possible that it does not have a manual movie mode.
Hopefully Xiaomi sticks to updating this camera for the long run so we may see custom picture profiles or any missing features. Will be interesting to get body-only as this is the cheapest m43 mount 4k camera.